/*

TITLE

    R-TREES: A DYNAMIC INDEX STRUCTURE FOR SPATIAL SEARCHING

DESCRIPTION

    A C++ templated version of the RTree algorithm.
    For more information please read the comments in RTree.h

AUTHORS

    * 1983 Original algorithm and test code by Antonin Guttman and Michael Stonebraker, UC Berkely
    * 1994 ANCI C ported from original test code by Melinda Green - melinda@superliminal.com
    * 1995 Sphere volume fix for degeneracy problem submitted by Paul Brook
    * 2004 Templated C++ port by Greg Douglas

LICENSE:

    Entirely free for all uses. Enjoy!

FILES
    * RTree.h            The C++ templated RTree implementation. Well commented.
    * Test.cpp           A simple test program, ported from the original C version.
    * MemoryTest.cpp     A more rigourous test to validate memory use.
    * README.TXT         This file.

TO BUILD

    To build a test, compile only one of the test files with RTree.h.
    Both test files contain a main() function.

RECENT CHANGE LOG

05 Jan 2010
o Fixed Iterator GetFirst() - Previous fix was not incomplete

03 Dec 2009
o Added Iteartor GetBounds()
o Added Iterator usage to simple test
o Fixed Iterator GetFirst() - Thanks Mathew Riek
o Minor updates for MSVC 2005/08 compilers

 */

#ifndef RTREE_H
#define RTREE_H
#include <algorithm>

// NOTE This file compiles under MSVC 6 SP5 and MSVC .Net 2003 it may not work on other compilers without modification.

// NOTE These next few lines may be win32 specific, you may need to modify them to compile on other platform
#include <stdio.h>
#include <math.h>
#include <assert.h>
#include <stdlib.h>

#define ASSERT assert // RTree uses ASSERT( condition )
//#ifndef Min
//  #define Min std::min
//#endif //Min
//#ifndef Max
//  #define Max std::max
//#endif //Max

//
// RTree.h
//

#define RTREE_TEMPLATE template<class DATATYPE, class ELEMTYPE, int NUMDIMS, class ELEMTYPEREAL, int TMAXNODES, int TMINNODES>
#define RTREE_QUAL RTree<DATATYPE, ELEMTYPE, NUMDIMS, ELEMTYPEREAL, TMAXNODES, TMINNODES>

#define RTREE_DONT_USE_MEMPOOLS // This version does not contain a fixed memory allocator, fill in lines with EXAMPLE to implement one.
#define RTREE_USE_SPHERICAL_VOLUME // Better split classification, may be slower on some systems

// Fwd decl
class RTFileStream;  // File I/O helper class, look below for implementation and notes.


/// \class RTree
/// Implementation of RTree, a multidimensional bounding rectangle tree.
/// Example usage: For a 3-dimensional tree use RTree<Object*, float, 3> myTree;
///
/// This modified, templated C++ version by Greg Douglas at Auran (http://www.auran.com)
///
/// DATATYPE Referenced data, should be int, void*, obj* etc. no larger than sizeof<void*> and simple type
/// ELEMTYPE Type of element such as int or float
/// NUMDIMS Number of dimensions such as 2 or 3
/// ELEMTYPEREAL Type of element that allows fractional and large values such as float or double, for use in volume calcs
///
/// NOTES: Inserting and removing data requires the knowledge of its constant Minimal Bounding Rectangle.
///        This version uses new/delete for nodes, I recommend using a fixed size allocator for efficiency.
///        Instead of using a callback function for returned results, I recommend and efficient pre-sized, grow-only memory
///        array similar to MFC CArray or STL Vector for returning search query result.
///
template<class DATATYPE, class ELEMTYPE, int NUMDIMS,
         class ELEMTYPEREAL = ELEMTYPE, int TMAXNODES = 8, int TMINNODES = TMAXNODES / 2>
class RTree
{
protected:

    struct Node;  // Fwd decl.  Used by other internal structs and iterator

public:

    // These constant must be declared after Branch and before Node struct
    // Stuck up here for MSVC 6 compiler.  NSVC .NET 2003 is much happier.
    enum
    {
        MAXNODES = TMAXNODES,                         ///< Max elements in node
        MINNODES = TMINNODES,                         ///< Min elements in node
    };


public:

    RTree();
    virtual ~RTree();

    /// Insert entry
    /// \param a_min Min of bounding rect
    /// \param a_max Max of bounding rect
    /// \param a_dataId Positive Id of data.  Maybe zero, but negative numbers not allowed.
    void Insert(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], const DATATYPE& a_dataId);

    /// Remove entry
    /// \param a_min Min of bounding rect
    /// \param a_max Max of bounding rect
    /// \param a_dataId Positive Id of data.  Maybe zero, but negative numbers not allowed.
    void Remove(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], const DATATYPE& a_dataId);

    /// Find all within search rectangle
    /// \param a_min Min of search bounding rect
    /// \param a_max Max of search bounding rect
    /// \param a_resultCallback Callback function to return result.  Callback should return 'true' to continue searching
    /// \param a_context User context to pass as parameter to a_resultCallback
    /// \return Returns the number of entries found
    int Search(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], bool a_resultCallback(DATATYPE a_data, void* a_context), void* a_context);

    /// Remove all entries from tree
    void RemoveAll();

    /// Count the data elements in this container.  This is slow as no internal counter is maintained.
    int Count();

    /// Load tree contents from file
    bool Load(const char* a_fileName);
    /// Load tree contents from stream
    bool Load(RTFileStream& a_stream);


    /// Save tree contents to file
    bool Save(const char* a_fileName);
    /// Save tree contents to stream
    bool Save(RTFileStream& a_stream);

    /// Iterator is not remove safe.
    class Iterator
    {
    private:

        enum { MAX_STACK = 32 }; //  Max stack size. Allows almost n^32 where n is number of branches in node

        struct StackElement
        {
            Node* m_node;
            int m_branchIndex;
        };

    public:

        Iterator()                                    { Init(); }

        ~Iterator()                                   { }

        /// Is iterator invalid
        bool IsNull()                                 { return (m_tos <= 0); }

        /// Is iterator pointing to valid data
        bool IsNotNull()                              { return (m_tos > 0); }

        /// Access the current data element. Caller must be sure iterator is not nullptr first.
        DATATYPE& operator*()
        {
            ASSERT(IsNotNull());
            StackElement& curTos = m_stack[m_tos - 1];
            return curTos.m_node->m_branch[curTos.m_branchIndex].m_data;
        }

        /// Access the current data element. Caller must be sure iterator is not nullptr first.
        const DATATYPE& operator*() const
        {
            ASSERT(IsNotNull());
            StackElement& curTos = m_stack[m_tos - 1];
            return curTos.m_node->m_branch[curTos.m_branchIndex].m_data;
        }

        /// Find the next data element
        bool operator++()                             { return FindNextData(); }

        /// Get the bounds for this node
        void GetBounds(ELEMTYPE a_min[NUMDIMS], ELEMTYPE a_max[NUMDIMS])
        {
            ASSERT(IsNotNull());
            StackElement& curTos = m_stack[m_tos - 1];
            Branch& curBranch = curTos.m_node->m_branch[curTos.m_branchIndex];

            for(int index = 0; index < NUMDIMS; ++index)
            {
                a_min[index] = curBranch.m_rect.m_min[index];
                a_max[index] = curBranch.m_rect.m_max[index];
            }
        }

    private:

        /// Reset iterator
        void Init()                                   { m_tos = 0; }

        /// Find the next data element in the tree (For internal use only)
        bool FindNextData()
        {
            for(;;)
            {
                if(m_tos <= 0)
                {
                    return false;
                }
                StackElement curTos = Pop(); // Copy stack top cause it may change as we use it

                if(curTos.m_node->IsLeaf())
                {
                    // Keep walking through data while we can
                    if(curTos.m_branchIndex+1 < curTos.m_node->m_count)
                    {
                        // There is more data, just point to the next one
                        Push(curTos.m_node, curTos.m_branchIndex + 1);
                        return true;
                    }
                    // No more data, so it will fall back to previous level
                }
                else
                {
                    if(curTos.m_branchIndex+1 < curTos.m_node->m_count)
                    {
                        // Push sibling on for future tree walk
                        // This is the 'fall back' node when we finish with the current level
                        Push(curTos.m_node, curTos.m_branchIndex + 1);
                    }
                    // Since cur node is not a leaf, push first of next level to get deeper into the tree
                    Node* nextLevelnode = curTos.m_node->m_branch[curTos.m_branchIndex].m_child;
                    Push(nextLevelnode, 0);

                    // If we pushed on a new leaf, exit as the data is ready at TOS
                    if(nextLevelnode->IsLeaf())
                    {
                        return true;
                    }
                }
            }
        }

        /// Push node and branch onto iteration stack (For internal use only)
        void Push(Node* a_node, int a_branchIndex)
        {
            m_stack[m_tos].m_node = a_node;
            m_stack[m_tos].m_branchIndex = a_branchIndex;
            ++m_tos;
            ASSERT(m_tos <= MAX_STACK);
        }

        /// Pop element off iteration stack (For internal use only)
        StackElement& Pop()
        {
            ASSERT(m_tos > 0);
            --m_tos;
            return m_stack[m_tos];
        }

        StackElement m_stack[MAX_STACK];              ///< Stack as we are doing iteration instead of recursion
        int m_tos;                                    ///< Top Of Stack index

        friend class RTree; // Allow hiding of non-public functions while allowing manipulation by logical owner
    };

    /// Get 'first' for iteration
    void GetFirst(Iterator& a_it)
    {
        a_it.Init();
        Node* first = m_root;
        while(first)
        {
            if(first->IsInternalNode() && first->m_count > 1)
            {
                a_it.Push(first, 1); // Descend sibling branch later
            }
            else if(first->IsLeaf())
            {
                if(first->m_count)
                {
                    a_it.Push(first, 0);
                }
                break;
            }
            first = first->m_branch[0].m_child;
        }
    }

    /// Get Next for iteration
    void GetNext(Iterator& a_it)                    { ++a_it; }

    /// Is iterator nullptr, or at end?
    bool IsNull(Iterator& a_it)                     { return a_it.IsNull(); }

    /// Get object at iterator position
    DATATYPE& GetAt(Iterator& a_it)                 { return *a_it; }

protected:

    /// Minimal bounding rectangle (n-dimensional)
    struct Rect
    {
        ELEMTYPE m_min[NUMDIMS];                      ///< Min dimensions of bounding box
        ELEMTYPE m_max[NUMDIMS];                      ///< Max dimensions of bounding box
    };

    /// May be data or may be another subtree
    /// The parents level determines this.
    /// If the parents level is 0, then this is data
    struct Branch
    {
        Rect m_rect;                                  ///< Bounds
        union
        {
            Node* m_child;                              ///< Child node
            DATATYPE m_data;                            ///< Data Id or Ptr
        };
    };

    /// Node for each branch level
    struct Node
    {
        bool IsInternalNode()                         { return (m_level > 0); } // Not a leaf, but a internal node
        bool IsLeaf()                                 { return (m_level == 0); } // A leaf, contains data

        int m_count;                                  ///< Count
        int m_level;                                  ///< Leaf is zero, others positive
        Branch m_branch[MAXNODES];                    ///< Branch
    };

    /// A link list of nodes for reinsertion after a delete operation
    struct ListNode
    {
        ListNode* m_next;                             ///< Next in list
        Node* m_node;                                 ///< Node
    };

    /// Variables for finding a split partition
    struct PartitionVars
    {
        int m_partition[MAXNODES+1];
        int m_total;
        int m_minFill;
        int m_taken[MAXNODES+1];
        int m_count[2];
        Rect m_cover[2];
        ELEMTYPEREAL m_area[2];

        Branch m_branchBuf[MAXNODES+1];
        int m_branchCount;
        Rect m_coverSplit;
        ELEMTYPEREAL m_coverSplitArea;
    };

    Node* AllocNode();
    void FreeNode(Node* a_node);
    void InitNode(Node* a_node);
    void InitRect(Rect* a_rect);
    bool InsertRectRec(Rect* a_rect, const DATATYPE& a_id, Node* a_node, Node** a_newNode, int a_level);
    bool InsertRect(Rect* a_rect, const DATATYPE& a_id, Node** a_root, int a_level);
    Rect NodeCover(Node* a_node);
    bool AddBranch(Branch* a_branch, Node* a_node, Node** a_newNode);
    void DisconnectBranch(Node* a_node, int a_index);
    int PickBranch(Rect* a_rect, Node* a_node);
    Rect CombineRect(Rect* a_rectA, Rect* a_rectB);
    void SplitNode(Node* a_node, Branch* a_branch, Node** a_newNode);
    ELEMTYPEREAL RectSphericalVolume(Rect* a_rect);
    ELEMTYPEREAL RectVolume(Rect* a_rect);
    ELEMTYPEREAL CalcRectVolume(Rect* a_rect);
    void GetBranches(Node* a_node, Branch* a_branch, PartitionVars* a_parVars);
    void ChoosePartition(PartitionVars* a_parVars, int a_minFill);
    void LoadNodes(Node* a_nodeA, Node* a_nodeB, PartitionVars* a_parVars);
    void InitParVars(PartitionVars* a_parVars, int a_maxRects, int a_minFill);
    void PickSeeds(PartitionVars* a_parVars);
    void Classify(int a_index, int a_group, PartitionVars* a_parVars);
    bool RemoveRect(Rect* a_rect, const DATATYPE& a_id, Node** a_root);
    bool RemoveRectRec(Rect* a_rect, const DATATYPE& a_id, Node* a_node, ListNode** a_listNode);
    ListNode* AllocListNode();
    void FreeListNode(ListNode* a_listNode);
    bool Overlap(Rect* a_rectA, Rect* a_rectB);
    void ReInsert(Node* a_node, ListNode** a_listNode);
    bool Search(Node* a_node, Rect* a_rect, int& a_foundCount, bool a_resultCallback(DATATYPE a_data, void* a_context), void* a_context);
    void RemoveAllRec(Node* a_node);
    void Reset();
    void CountRec(Node* a_node, int& a_count);

    bool SaveRec(Node* a_node, RTFileStream& a_stream);
    bool LoadRec(Node* a_node, RTFileStream& a_stream);

    Node* m_root;                                    ///< Root of tree
    ELEMTYPEREAL m_unitSphereVolume;                 ///< Unit sphere constant for required number of dimensions
};


// Because there is not stream support, this is a quick and dirty file I/O helper.
// Users will likely replace its usage with a Stream implementation from their favorite API.
class RTFileStream
{
    FILE* m_file;

public:


    RTFileStream()
    {
        m_file = nullptr;
    }

    ~RTFileStream()
    {
        Close();
    }

    bool OpenRead(const char* a_fileName)
    {
        m_file = fopen(a_fileName, "rb");
        if(!m_file)
        {
            return false;
        }
        return true;
    }

    bool OpenWrite(const char* a_fileName)
    {
        m_file = fopen(a_fileName, "wb");
        if(!m_file)
        {
            return false;
        }
        return true;
    }

    void Close()
    {
        if(m_file)
        {
            fclose(m_file);
            m_file = nullptr;
        }
    }

    template< typename TYPE >
    size_t Write(const TYPE& a_value)
    {
        ASSERT(m_file);
        return fwrite((void*)&a_value, sizeof(a_value), 1, m_file);
    }

    template< typename TYPE >
    size_t WriteArray(const TYPE* a_array, int a_count)
    {
        ASSERT(m_file);
        return fwrite((void*)a_array, sizeof(TYPE) * a_count, 1, m_file);
    }

    template< typename TYPE >
    size_t Read(TYPE& a_value)
    {
        ASSERT(m_file);
        return fread((void*)&a_value, sizeof(a_value), 1, m_file);
    }

    template< typename TYPE >
    size_t ReadArray(TYPE* a_array, int a_count)
    {
        ASSERT(m_file);
        return fread((void*)a_array, sizeof(TYPE) * a_count, 1, m_file);
    }
};


RTREE_TEMPLATE
RTREE_QUAL::RTree()
{
    ASSERT(MAXNODES > MINNODES);
    ASSERT(MINNODES > 0);


    // We only support machine word size simple data type eg. integer index or object pointer.
    // Since we are storing as union with non data branch
    ASSERT(sizeof(DATATYPE) == sizeof(void*) || sizeof(DATATYPE) == sizeof(int));

    // Precomputed volumes of the unit spheres for the first few dimensions
    const float UNIT_SPHERE_VOLUMES[] = {
        0.000000f, 2.000000f, 3.141593f, // Dimension  0,1,2
        4.188790f, 4.934802f, 5.263789f, // Dimension  3,4,5
        5.167713f, 4.724766f, 4.058712f, // Dimension  6,7,8
        3.298509f, 2.550164f, 1.884104f, // Dimension  9,10,11
        1.335263f, 0.910629f, 0.599265f, // Dimension  12,13,14
        0.381443f, 0.235331f, 0.140981f, // Dimension  15,16,17
        0.082146f, 0.046622f, 0.025807f, // Dimension  18,19,20
    };

    m_root = AllocNode();
    m_root->m_level = 0;
    m_unitSphereVolume = (ELEMTYPEREAL)UNIT_SPHERE_VOLUMES[NUMDIMS];
}


RTREE_TEMPLATE
RTREE_QUAL::~RTree()
{
    Reset(); // Free, or reset node memory
}


RTREE_TEMPLATE
void RTREE_QUAL::Insert(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], const DATATYPE& a_dataId)
{
#ifdef _DEBUG
    for(int index=0; index<NUMDIMS; ++index)
    {
        ASSERT(a_min[index] <= a_max[index]);
    }
#endif //_DEBUG

    Rect rect;

    for(int axis=0; axis<NUMDIMS; ++axis)
    {
        rect.m_min[axis] = a_min[axis];
        rect.m_max[axis] = a_max[axis];
    }

    InsertRect(&rect, a_dataId, &m_root, 0);
}


RTREE_TEMPLATE
void RTREE_QUAL::Remove(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], const DATATYPE& a_dataId)
{
#ifdef _DEBUG
    for(int index=0; index<NUMDIMS; ++index)
    {
        ASSERT(a_min[index] <= a_max[index]);
    }
#endif //_DEBUG

    Rect rect;

    for(int axis=0; axis<NUMDIMS; ++axis)
    {
        rect.m_min[axis] = a_min[axis];
        rect.m_max[axis] = a_max[axis];
    }

    RemoveRect(&rect, a_dataId, &m_root);
}


RTREE_TEMPLATE
int RTREE_QUAL::Search(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], bool a_resultCallback(DATATYPE a_data, void* a_context), void* a_context)
{
#ifdef _DEBUG
    for(int index=0; index<NUMDIMS; ++index)
    {
        ASSERT(a_min[index] <= a_max[index]);
    }
#endif //_DEBUG

    Rect rect;

    for(int axis=0; axis<NUMDIMS; ++axis)
    {
        rect.m_min[axis] = a_min[axis];
        rect.m_max[axis] = a_max[axis];
    }

    // NOTE: May want to return search result another way, perhaps returning the number of found elements here.

    int foundCount = 0;
    Search(m_root, &rect, foundCount, a_resultCallback, a_context);

    return foundCount;
}


RTREE_TEMPLATE
int RTREE_QUAL::Count()
{
    int count = 0;
    CountRec(m_root, count);

    return count;
}



RTREE_TEMPLATE
void RTREE_QUAL::CountRec(Node* a_node, int& a_count)
{
    if(a_node->IsInternalNode())  // not a leaf node
    {
        for(int index = 0; index < a_node->m_count; ++index)
        {
            CountRec(a_node->m_branch[index].m_child, a_count);
        }
    }
    else // A leaf node
    {
        a_count += a_node->m_count;
    }
}


RTREE_TEMPLATE
bool RTREE_QUAL::Load(const char* a_fileName)
{
    RemoveAll(); // Clear existing tree

    RTFileStream stream;
    if(!stream.OpenRead(a_fileName))
    {
        return false;
    }

    bool result = Load(stream);

    stream.Close();

    return result;
};



RTREE_TEMPLATE
bool RTREE_QUAL::Load(RTFileStream& a_stream)
{
    // Write some kind of header
    int _dataFileId = ('R'<<0)|('T'<<8)|('R'<<16)|('E'<<24);
    int _dataSize = sizeof(DATATYPE);
    int _dataNumDims = NUMDIMS;
    int _dataElemSize = sizeof(ELEMTYPE);
    int _dataElemRealSize = sizeof(ELEMTYPEREAL);
    int _dataMaxNodes = TMAXNODES;
    int _dataMinNodes = TMINNODES;

    int dataFileId = 0;
    int dataSize = 0;
    int dataNumDims = 0;
    int dataElemSize = 0;
    int dataElemRealSize = 0;
    int dataMaxNodes = 0;
    int dataMinNodes = 0;

    a_stream.Read(dataFileId);
    a_stream.Read(dataSize);
    a_stream.Read(dataNumDims);
    a_stream.Read(dataElemSize);
    a_stream.Read(dataElemRealSize);
    a_stream.Read(dataMaxNodes);
    a_stream.Read(dataMinNodes);

    bool result = false;

    // Test if header was valid and compatible
    if(    (dataFileId == _dataFileId)
           && (dataSize == _dataSize)
           && (dataNumDims == _dataNumDims)
           && (dataElemSize == _dataElemSize)
           && (dataElemRealSize == _dataElemRealSize)
           && (dataMaxNodes == _dataMaxNodes)
           && (dataMinNodes == _dataMinNodes)
           )
    {
        // Recursively load tree
        result = LoadRec(m_root, a_stream);
    }

    return result;
}


RTREE_TEMPLATE
bool RTREE_QUAL::LoadRec(Node* a_node, RTFileStream& a_stream)
{
    a_stream.Read(a_node->m_level);
    a_stream.Read(a_node->m_count);

    if(a_node->IsInternalNode())  // not a leaf node
    {
        for(int index = 0; index < a_node->m_count; ++index)
        {
            Branch* curBranch = &a_node->m_branch[index];

            a_stream.ReadArray(curBranch->m_rect.m_min, NUMDIMS);
            a_stream.ReadArray(curBranch->m_rect.m_max, NUMDIMS);

            curBranch->m_child = AllocNode();
            LoadRec(curBranch->m_child, a_stream);
        }
    }
    else // A leaf node
    {
        for(int index = 0; index < a_node->m_count; ++index)
        {
            Branch* curBranch = &a_node->m_branch[index];

            a_stream.ReadArray(curBranch->m_rect.m_min, NUMDIMS);
            a_stream.ReadArray(curBranch->m_rect.m_max, NUMDIMS);

            a_stream.Read(curBranch->m_data);
        }
    }

    return true; // Should do more error checking on I/O operations
}


RTREE_TEMPLATE
bool RTREE_QUAL::Save(const char* a_fileName)
{
    RTFileStream stream;
    if(!stream.OpenWrite(a_fileName))
    {
        return false;
    }

    bool result = Save(stream);

    stream.Close();

    return result;
}


RTREE_TEMPLATE
bool RTREE_QUAL::Save(RTFileStream& a_stream)
{
    // Write some kind of header
    int dataFileId = ('R'<<0)|('T'<<8)|('R'<<16)|('E'<<24);
    int dataSize = sizeof(DATATYPE);
    int dataNumDims = NUMDIMS;
    int dataElemSize = sizeof(ELEMTYPE);
    int dataElemRealSize = sizeof(ELEMTYPEREAL);
    int dataMaxNodes = TMAXNODES;
    int dataMinNodes = TMINNODES;

    a_stream.Write(dataFileId);
    a_stream.Write(dataSize);
    a_stream.Write(dataNumDims);
    a_stream.Write(dataElemSize);
    a_stream.Write(dataElemRealSize);
    a_stream.Write(dataMaxNodes);
    a_stream.Write(dataMinNodes);

    // Recursively save tree
    bool result = SaveRec(m_root, a_stream);

    return result;
}


RTREE_TEMPLATE
bool RTREE_QUAL::SaveRec(Node* a_node, RTFileStream& a_stream)
{
    a_stream.Write(a_node->m_level);
    a_stream.Write(a_node->m_count);

    if(a_node->IsInternalNode())  // not a leaf node
    {
        for(int index = 0; index < a_node->m_count; ++index)
        {
            Branch* curBranch = &a_node->m_branch[index];

            a_stream.WriteArray(curBranch->m_rect.m_min, NUMDIMS);
            a_stream.WriteArray(curBranch->m_rect.m_max, NUMDIMS);

            SaveRec(curBranch->m_child, a_stream);
        }
    }
    else // A leaf node
    {
        for(int index = 0; index < a_node->m_count; ++index)
        {
            Branch* curBranch = &a_node->m_branch[index];

            a_stream.WriteArray(curBranch->m_rect.m_min, NUMDIMS);
            a_stream.WriteArray(curBranch->m_rect.m_max, NUMDIMS);

            a_stream.Write(curBranch->m_data);
        }
    }

    return true; // Should do more error checking on I/O operations
}


RTREE_TEMPLATE
void RTREE_QUAL::RemoveAll()
{
    // Delete all existing nodes
    Reset();

    m_root = AllocNode();
    m_root->m_level = 0;
}


RTREE_TEMPLATE
void RTREE_QUAL::Reset()
{
#ifdef RTREE_DONT_USE_MEMPOOLS
    // Delete all existing nodes
    RemoveAllRec(m_root);
#else // RTREE_DONT_USE_MEMPOOLS
    // Just reset memory pools.  We are not using complex types
    // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
}


RTREE_TEMPLATE
void RTREE_QUAL::RemoveAllRec(Node* a_node)
{
    ASSERT(a_node);
    ASSERT(a_node->m_level >= 0);

    if(a_node->IsInternalNode()) // This is an internal node in the tree
    {
        for(int index=0; index < a_node->m_count; ++index)
        {
            RemoveAllRec(a_node->m_branch[index].m_child);
        }
    }
    FreeNode(a_node);
}


RTREE_TEMPLATE
typename RTREE_QUAL::Node* RTREE_QUAL::AllocNode()
{
    Node* newNode;
#ifdef RTREE_DONT_USE_MEMPOOLS
    newNode = new Node;
#else // RTREE_DONT_USE_MEMPOOLS
    // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
    InitNode(newNode);
    return newNode;
}


RTREE_TEMPLATE
void RTREE_QUAL::FreeNode(Node* a_node)
{
    ASSERT(a_node);

#ifdef RTREE_DONT_USE_MEMPOOLS
    delete a_node;
#else // RTREE_DONT_USE_MEMPOOLS
    // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
}


// Allocate space for a node in the list used in DeletRect to
// store Nodes that are too empty.
RTREE_TEMPLATE
typename RTREE_QUAL::ListNode* RTREE_QUAL::AllocListNode()
{
#ifdef RTREE_DONT_USE_MEMPOOLS
    return new ListNode;
#else // RTREE_DONT_USE_MEMPOOLS
    // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
}


RTREE_TEMPLATE
void RTREE_QUAL::FreeListNode(ListNode* a_listNode)
{
#ifdef RTREE_DONT_USE_MEMPOOLS
    delete a_listNode;
#else // RTREE_DONT_USE_MEMPOOLS
    // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
}


RTREE_TEMPLATE
void RTREE_QUAL::InitNode(Node* a_node)
{
    a_node->m_count = 0;
    a_node->m_level = -1;
}


RTREE_TEMPLATE
void RTREE_QUAL::InitRect(Rect* a_rect)
{
    for(int index = 0; index < NUMDIMS; ++index)
    {
        a_rect->m_min[index] = (ELEMTYPE)0;
        a_rect->m_max[index] = (ELEMTYPE)0;
    }
}


// Inserts a new data rectangle into the index structure.
// Recursively descends tree, propagates splits back up.
// Returns 0 if node was not split.  Old node updated.
// If node was split, returns 1 and sets the pointer pointed to by
// new_node to point to the new node.  Old node updated to become one of two.
// The level argument specifies the number of steps up from the leaf
// level to insert; e.g. a data rectangle goes in at level = 0.
RTREE_TEMPLATE
bool RTREE_QUAL::InsertRectRec(Rect* a_rect, const DATATYPE& a_id, Node* a_node, Node** a_newNode, int a_level)
{
    ASSERT(a_rect && a_node && a_newNode);
    ASSERT(a_level >= 0 && a_level <= a_node->m_level);

    int index;
    Branch branch;
    Node* otherNode;

    // Still above level for insertion, go down tree recursively
    if(a_node->m_level > a_level)
    {
        index = PickBranch(a_rect, a_node);

        if(index < 0) return false; // Added for Gmsh

        if (!InsertRectRec(a_rect, a_id, a_node->m_branch[index].m_child, &otherNode, a_level))
        {
            // Child was not split
            a_node->m_branch[index].m_rect = CombineRect(a_rect, &(a_node->m_branch[index].m_rect));
            return false;
        }
        else // Child was split
        {
            a_node->m_branch[index].m_rect = NodeCover(a_node->m_branch[index].m_child);
            branch.m_child = otherNode;
            branch.m_rect = NodeCover(otherNode);
            return AddBranch(&branch, a_node, a_newNode);
        }
    }
    else if(a_node->m_level == a_level) // Have reached level for insertion. Add rect, split if necessary
    {
        branch.m_rect = *a_rect;
        branch.m_child = (Node*) a_id;
        // Child field of leaves contains id of data record
        return AddBranch(&branch, a_node, a_newNode);
    }
    else
    {
        // Should never occur
        ASSERT(0);
        return false;
    }
}


// Insert a data rectangle into an index structure.
// InsertRect provides for splitting the root;
// returns 1 if root was split, 0 if it was not.
// The level argument specifies the number of steps up from the leaf
// level to insert; e.g. a data rectangle goes in at level = 0.
// InsertRect2 does the recursion.
//
RTREE_TEMPLATE
bool RTREE_QUAL::InsertRect(Rect* a_rect, const DATATYPE& a_id, Node** a_root, int a_level)
{
    ASSERT(a_rect && a_root);
    ASSERT(a_level >= 0 && a_level <= (*a_root)->m_level);
#ifdef _DEBUG
    for(int index=0; index < NUMDIMS; ++index)
    {
        ASSERT(a_rect->m_min[index] <= a_rect->m_max[index]);
    }
#endif //_DEBUG

    Node* newRoot;
    Node* newNode;
    Branch branch;

    if(InsertRectRec(a_rect, a_id, *a_root, &newNode, a_level))  // Root split
    {
        newRoot = AllocNode();  // Grow tree taller and new root
        newRoot->m_level = (*a_root)->m_level + 1;
        branch.m_rect = NodeCover(*a_root);
        branch.m_child = *a_root;
        AddBranch(&branch, newRoot, nullptr);
        branch.m_rect = NodeCover(newNode);
        branch.m_child = newNode;
        AddBranch(&branch, newRoot, nullptr);
        *a_root = newRoot;
        return true;
    }

    return false;
}


// Find the smallest rectangle that includes all rectangles in branches of a node.
RTREE_TEMPLATE
typename RTREE_QUAL::Rect RTREE_QUAL::NodeCover(Node* a_node)
{
    ASSERT(a_node);

    int firstTime = true;
    Rect rect;
    InitRect(&rect);

    for(int index = 0; index < a_node->m_count; ++index)
    {
        if(firstTime)
        {
            rect = a_node->m_branch[index].m_rect;
            firstTime = false;
        }
        else
        {
            rect = CombineRect(&rect, &(a_node->m_branch[index].m_rect));
        }
    }

    return rect;
}


// Add a branch to a node.  Split the node if necessary.
// Returns 0 if node not split.  Old node updated.
// Returns 1 if node split, sets *new_node to address of new node.
// Old node updated, becomes one of two.
RTREE_TEMPLATE
bool RTREE_QUAL::AddBranch(Branch* a_branch, Node* a_node, Node** a_newNode)
{
    ASSERT(a_branch);
    ASSERT(a_node);

    if(a_node->m_count < MAXNODES)  // Split won't be necessary
    {
        a_node->m_branch[a_node->m_count] = *a_branch;
        ++a_node->m_count;

        return false;
    }
    else
    {
        ASSERT(a_newNode);

        SplitNode(a_node, a_branch, a_newNode);
        return true;
    }
}


// Disconnect a dependent node.
// Caller must return (or stop using iteration index) after this as count has changed
RTREE_TEMPLATE
void RTREE_QUAL::DisconnectBranch(Node* a_node, int a_index)
{
    ASSERT(a_node && (a_index >= 0) && (a_index < MAXNODES));
    ASSERT(a_node->m_count > 0);

    // Remove element by swapping with the last element to prevent gaps in array
    a_node->m_branch[a_index] = a_node->m_branch[a_node->m_count - 1];

    --a_node->m_count;
}


// Pick a branch.  Pick the one that will need the smallest increase
// in area to accomodate the new rectangle.  This will result in the
// least total area for the covering rectangles in the current node.
// In case of a tie, pick the one which was smaller before, to get
// the best resolution when searching.
RTREE_TEMPLATE
int RTREE_QUAL::PickBranch(Rect* a_rect, Node* a_node)
{
    ASSERT(a_rect && a_node);

    bool firstTime = true;
    ELEMTYPEREAL increase;
    ELEMTYPEREAL bestIncr = (ELEMTYPEREAL)-1;
    ELEMTYPEREAL area;
    ELEMTYPEREAL bestArea = (ELEMTYPEREAL)-1;
    int best = -1;
    Rect tempRect;

    for(int index=0; index < a_node->m_count; ++index)
    {
        Rect* curRect = &a_node->m_branch[index].m_rect;
        area = CalcRectVolume(curRect);
        tempRect = CombineRect(a_rect, curRect);
        increase = CalcRectVolume(&tempRect) - area;
        if((increase < bestIncr) || firstTime)
        {
            best = index;
            bestArea = area;
            bestIncr = increase;
            firstTime = false;
        }
        else if((increase == bestIncr) && (area < bestArea))
        {
            best = index;
            bestArea = area;
            bestIncr = increase;
        }
    }
    return best;
}


// Combine two rectangles into larger one containing both
RTREE_TEMPLATE
typename RTREE_QUAL::Rect RTREE_QUAL::CombineRect(Rect* a_rectA, Rect* a_rectB)
{
    ASSERT(a_rectA && a_rectB);

    Rect newRect;

    for(int index = 0; index < NUMDIMS; ++index)
    {
        newRect.m_min[index] = std::min(a_rectA->m_min[index], a_rectB->m_min[index]);
        newRect.m_max[index] = std::max(a_rectA->m_max[index], a_rectB->m_max[index]);
    }

    return newRect;
}



// Split a node.
// Divides the nodes branches and the extra one between two nodes.
// Old node is one of the new ones, and one really new one is created.
// Tries more than one method for choosing a partition, uses best result.
RTREE_TEMPLATE
void RTREE_QUAL::SplitNode(Node* a_node, Branch* a_branch, Node** a_newNode)
{
    ASSERT(a_node);
    ASSERT(a_branch);

    // Could just use local here, but member or external is faster since it is reused
    PartitionVars localVars;
    PartitionVars* parVars = &localVars;
    int level;

    // Load all the branches into a buffer, initialize old node
    level = a_node->m_level;
    GetBranches(a_node, a_branch, parVars);

    // Find partition
    ChoosePartition(parVars, MINNODES);

    // Put branches from buffer into 2 nodes according to chosen partition
    *a_newNode = AllocNode();
    (*a_newNode)->m_level = a_node->m_level = level;
    LoadNodes(a_node, *a_newNode, parVars);

    ASSERT((a_node->m_count + (*a_newNode)->m_count) == parVars->m_total);
}


// Calculate the n-dimensional volume of a rectangle
RTREE_TEMPLATE
ELEMTYPEREAL RTREE_QUAL::RectVolume(Rect* a_rect)
{
    ASSERT(a_rect);

    ELEMTYPEREAL volume = (ELEMTYPEREAL)1;

    for(int index=0; index<NUMDIMS; ++index)
    {
        volume *= a_rect->m_max[index] - a_rect->m_min[index];
    }

    ASSERT(volume >= (ELEMTYPEREAL)0);

    return volume;
}


// The exact volume of the bounding sphere for the given Rect
RTREE_TEMPLATE
ELEMTYPEREAL RTREE_QUAL::RectSphericalVolume(Rect* a_rect)
{
    ASSERT(a_rect);

    ELEMTYPEREAL sumOfSquares = (ELEMTYPEREAL)0;
    ELEMTYPEREAL radius;

    for(int index=0; index < NUMDIMS; ++index)
    {
        ELEMTYPEREAL halfExtent = ((ELEMTYPEREAL)a_rect->m_max[index] - (ELEMTYPEREAL)a_rect->m_min[index]) * 0.5f;
        sumOfSquares += halfExtent * halfExtent;
    }

    radius = (ELEMTYPEREAL)sqrt(sumOfSquares);

    // Pow maybe slow, so test for common dims like 2,3 and just use x*x, x*x*x.
    if(NUMDIMS == 3)
    {
        return (radius * radius * radius * m_unitSphereVolume);
    }
    else if(NUMDIMS == 2)
    {
        return (radius * radius * m_unitSphereVolume);
    }
    else
    {
        return (ELEMTYPEREAL)(pow(radius, NUMDIMS) * m_unitSphereVolume);
    }
}


// Use one of the methods to calculate retangle volume
RTREE_TEMPLATE
ELEMTYPEREAL RTREE_QUAL::CalcRectVolume(Rect* a_rect)
{
#ifdef RTREE_USE_SPHERICAL_VOLUME
    return RectSphericalVolume(a_rect); // Slower but helps certain merge cases
#else // RTREE_USE_SPHERICAL_VOLUME
    return RectVolume(a_rect); // Faster but can cause poor merges
#endif // RTREE_USE_SPHERICAL_VOLUME
}


// Load branch buffer with branches from full node plus the extra branch.
RTREE_TEMPLATE
void RTREE_QUAL::GetBranches(Node* a_node, Branch* a_branch, PartitionVars* a_parVars)
{
    ASSERT(a_node);
    ASSERT(a_branch);

    ASSERT(a_node->m_count == MAXNODES);

    // Load the branch buffer
    for(int index=0; index < MAXNODES; ++index)
    {
        a_parVars->m_branchBuf[index] = a_node->m_branch[index];
    }
    a_parVars->m_branchBuf[MAXNODES] = *a_branch;
    a_parVars->m_branchCount = MAXNODES + 1;

    // Calculate rect containing all in the set
    a_parVars->m_coverSplit = a_parVars->m_branchBuf[0].m_rect;
    for(int index=1; index < MAXNODES+1; ++index)
    {
        a_parVars->m_coverSplit = CombineRect(&a_parVars->m_coverSplit, &a_parVars->m_branchBuf[index].m_rect);
    }
    a_parVars->m_coverSplitArea = CalcRectVolume(&a_parVars->m_coverSplit);

    InitNode(a_node);
}


// Method #0 for choosing a partition:
// As the seeds for the two groups, pick the two rects that would waste the
// most area if covered by a single rectangle, i.e. evidently the worst pair
// to have in the same group.
// Of the remaining, one at a time is chosen to be put in one of the two groups.
// The one chosen is the one with the greatest difference in area expansion
// depending on which group - the rect most strongly attracted to one group
// and repelled from the other.
// If one group gets too full (more would force other group to violate min
// fill requirement) then other group gets the rest.
// These last are the ones that can go in either group most easily.
RTREE_TEMPLATE
void RTREE_QUAL::ChoosePartition(PartitionVars* a_parVars, int a_minFill)
{
    ASSERT(a_parVars);

    ELEMTYPEREAL biggestDiff;
    int group, chosen = -1, betterGroup = -1;

    InitParVars(a_parVars, a_parVars->m_branchCount, a_minFill);
    PickSeeds(a_parVars);

    while (((a_parVars->m_count[0] + a_parVars->m_count[1]) < a_parVars->m_total)
           && (a_parVars->m_count[0] < (a_parVars->m_total - a_parVars->m_minFill))
           && (a_parVars->m_count[1] < (a_parVars->m_total - a_parVars->m_minFill)))
    {
        biggestDiff = (ELEMTYPEREAL) -1;
        for(int index=0; index<a_parVars->m_total; ++index)
        {
            if(!a_parVars->m_taken[index])
            {
                Rect* curRect = &a_parVars->m_branchBuf[index].m_rect;
                Rect rect0 = CombineRect(curRect, &a_parVars->m_cover[0]);
                Rect rect1 = CombineRect(curRect, &a_parVars->m_cover[1]);
                ELEMTYPEREAL growth0 = CalcRectVolume(&rect0) - a_parVars->m_area[0];
                ELEMTYPEREAL growth1 = CalcRectVolume(&rect1) - a_parVars->m_area[1];
                ELEMTYPEREAL diff = growth1 - growth0;
                if(diff >= 0)
                {
                    group = 0;
                }
                else
                {
                    group = 1;
                    diff = -diff;
                }

                if(diff > biggestDiff)
                {
                    biggestDiff = diff;
                    chosen = index;
                    betterGroup = group;
                }
                else if((diff == biggestDiff) && (a_parVars->m_count[group] < a_parVars->m_count[betterGroup]))
                {
                    chosen = index;
                    betterGroup = group;
                }
            }
        }
        Classify(chosen, betterGroup, a_parVars);
    }

    // If one group too full, put remaining rects in the other
    if((a_parVars->m_count[0] + a_parVars->m_count[1]) < a_parVars->m_total)
    {
        if(a_parVars->m_count[0] >= a_parVars->m_total - a_parVars->m_minFill)
        {
            group = 1;
        }
        else
        {
            group = 0;
        }
        for(int index=0; index<a_parVars->m_total; ++index)
        {
            if(!a_parVars->m_taken[index])
            {
                Classify(index, group, a_parVars);
            }
        }
    }

    ASSERT((a_parVars->m_count[0] + a_parVars->m_count[1]) == a_parVars->m_total);
    ASSERT((a_parVars->m_count[0] >= a_parVars->m_minFill) &&
            (a_parVars->m_count[1] >= a_parVars->m_minFill));
}


// Copy branches from the buffer into two nodes according to the partition.
RTREE_TEMPLATE
void RTREE_QUAL::LoadNodes(Node* a_nodeA, Node* a_nodeB, PartitionVars* a_parVars)
{
    ASSERT(a_nodeA);
    ASSERT(a_nodeB);
    ASSERT(a_parVars);

    for(int index=0; index < a_parVars->m_total; ++index)
    {
        ASSERT(a_parVars->m_partition[index] == 0 || a_parVars->m_partition[index] == 1);

        if(a_parVars->m_partition[index] == 0)
        {
            AddBranch(&a_parVars->m_branchBuf[index], a_nodeA, nullptr);
        }
        else if(a_parVars->m_partition[index] == 1)
        {
            AddBranch(&a_parVars->m_branchBuf[index], a_nodeB, nullptr);
        }
    }
}


// Initialize a PartitionVars structure.
RTREE_TEMPLATE
void RTREE_QUAL::InitParVars(PartitionVars* a_parVars, int a_maxRects, int a_minFill)
{
    ASSERT(a_parVars);

    a_parVars->m_count[0] = a_parVars->m_count[1] = 0;
    a_parVars->m_area[0] = a_parVars->m_area[1] = (ELEMTYPEREAL)0;
    a_parVars->m_total = a_maxRects;
    a_parVars->m_minFill = a_minFill;
    for(int index=0; index < a_maxRects; ++index)
    {
        a_parVars->m_taken[index] = false;
        a_parVars->m_partition[index] = -1;
    }
}


RTREE_TEMPLATE
void RTREE_QUAL::PickSeeds(PartitionVars* a_parVars)
{
    int seed0 = -1, seed1 = -1;
    ELEMTYPEREAL worst, waste;
    ELEMTYPEREAL area[MAXNODES+1];

    for(int index=0; index<a_parVars->m_total; ++index)
    {
        area[index] = CalcRectVolume(&a_parVars->m_branchBuf[index].m_rect);
    }

    worst = -a_parVars->m_coverSplitArea - 1;
    for(int indexA=0; indexA < a_parVars->m_total-1; ++indexA)
    {
        for(int indexB = indexA+1; indexB < a_parVars->m_total; ++indexB)
        {
            Rect oneRect = CombineRect(&a_parVars->m_branchBuf[indexA].m_rect, &a_parVars->m_branchBuf[indexB].m_rect);
            waste = CalcRectVolume(&oneRect) - area[indexA] - area[indexB];
            if(waste > worst)
            {
                worst = waste;
                seed0 = indexA;
                seed1 = indexB;
            }
        }
    }
    Classify(seed0, 0, a_parVars);
    Classify(seed1, 1, a_parVars);
}


// Put a branch in one of the groups.
RTREE_TEMPLATE
void RTREE_QUAL::Classify(int a_index, int a_group, PartitionVars* a_parVars)
{
    ASSERT(a_parVars);
    ASSERT(!a_parVars->m_taken[a_index]);
    ASSERT(a_index >= 0); // Added for Gmsh

    a_parVars->m_partition[a_index] = a_group;
    a_parVars->m_taken[a_index] = true;

    if (a_parVars->m_count[a_group] == 0)
    {
        a_parVars->m_cover[a_group] = a_parVars->m_branchBuf[a_index].m_rect;
    }
    else
    {
        a_parVars->m_cover[a_group] = CombineRect(&a_parVars->m_branchBuf[a_index].m_rect, &a_parVars->m_cover[a_group]);
    }
    a_parVars->m_area[a_group] = CalcRectVolume(&a_parVars->m_cover[a_group]);
    ++a_parVars->m_count[a_group];
}


// Delete a data rectangle from an index structure.
// Pass in a pointer to a Rect, the tid of the record, ptr to ptr to root node.
// Returns 1 if record not found, 0 if success.
// RemoveRect provides for eliminating the root.
RTREE_TEMPLATE
bool RTREE_QUAL::RemoveRect(Rect* a_rect, const DATATYPE& a_id, Node** a_root)
{
    ASSERT(a_rect && a_root);
    ASSERT(*a_root);

    Node* tempNode;
    ListNode* reInsertList = nullptr;

    if(!RemoveRectRec(a_rect, a_id, *a_root, &reInsertList))
    {
        // Found and deleted a data item
        // Reinsert any branches from eliminated nodes
        while(reInsertList)
        {
            tempNode = reInsertList->m_node;

            for(int index = 0; index < tempNode->m_count; ++index)
            {
                InsertRect(&(tempNode->m_branch[index].m_rect),
                           tempNode->m_branch[index].m_data,
                           a_root,
                           tempNode->m_level);
            }

            ListNode* remLNode = reInsertList;
            reInsertList = reInsertList->m_next;

            FreeNode(remLNode->m_node);
            FreeListNode(remLNode);
        }

        // Check for redundant root (not leaf, 1 child) and eliminate
        if((*a_root)->m_count == 1 && (*a_root)->IsInternalNode())
        {
            tempNode = (*a_root)->m_branch[0].m_child;

            ASSERT(tempNode);
            FreeNode(*a_root);
            *a_root = tempNode;
        }
        return false;
    }
    else
    {
        return true;
    }
}


// Delete a rectangle from non-root part of an index structure.
// Called by RemoveRect.  Descends tree recursively,
// merges branches on the way back up.
// Returns 1 if record not found, 0 if success.
RTREE_TEMPLATE
bool RTREE_QUAL::RemoveRectRec(Rect* a_rect, const DATATYPE& a_id, Node* a_node, ListNode** a_listNode)
{
    ASSERT(a_rect && a_node && a_listNode);
    ASSERT(a_node->m_level >= 0);

    if(a_node->IsInternalNode())  // not a leaf node
    {
        for(int index = 0; index < a_node->m_count; ++index)
        {
            if(Overlap(a_rect, &(a_node->m_branch[index].m_rect)))
            {
                if(!RemoveRectRec(a_rect, a_id, a_node->m_branch[index].m_child, a_listNode))
                {
                    if(a_node->m_branch[index].m_child->m_count >= MINNODES)
                    {
                        // child removed, just resize parent rect
                        a_node->m_branch[index].m_rect = NodeCover(a_node->m_branch[index].m_child);
                    }
                    else
                    {
                        // child removed, not enough entries in node, eliminate node
                        ReInsert(a_node->m_branch[index].m_child, a_listNode);
                        DisconnectBranch(a_node, index); // Must return after this call as count has changed
                    }
                    return false;
                }
            }
        }
        return true;
    }
    else // A leaf node
    {
        for(int index = 0; index < a_node->m_count; ++index)
        {
            if(a_node->m_branch[index].m_child == (Node*)a_id)
            {
                DisconnectBranch(a_node, index); // Must return after this call as count has changed
                return false;
            }
        }
        return true;
    }
}


// Decide whether two rectangles overlap.
RTREE_TEMPLATE
bool RTREE_QUAL::Overlap(Rect* a_rectA, Rect* a_rectB)
{
    ASSERT(a_rectA && a_rectB);

    for(int index=0; index < NUMDIMS; ++index)
    {
        if (a_rectA->m_min[index] > a_rectB->m_max[index] ||
                a_rectB->m_min[index] > a_rectA->m_max[index])
        {
            return false;
        }
    }
    return true;
}


// Add a node to the reinsertion list.  All its branches will later
// be reinserted into the index structure.
RTREE_TEMPLATE
void RTREE_QUAL::ReInsert(Node* a_node, ListNode** a_listNode)
{
    ListNode* newListNode;

    newListNode = AllocListNode();
    newListNode->m_node = a_node;
    newListNode->m_next = *a_listNode;
    *a_listNode = newListNode;
}


// Search in an index tree or subtree for all data retangles that overlap the argument rectangle.
RTREE_TEMPLATE
bool RTREE_QUAL::Search(Node* a_node, Rect* a_rect, int& a_foundCount, bool a_resultCallback(DATATYPE a_data, void* a_context), void* a_context)
{
    ASSERT(a_node);
    ASSERT(a_node->m_level >= 0);
    ASSERT(a_rect);

    if(a_node->IsInternalNode()) // This is an internal node in the tree
    {
        for(int index=0; index < a_node->m_count; ++index)
        {
            if(Overlap(a_rect, &a_node->m_branch[index].m_rect))
            {
                if(!Search(a_node->m_branch[index].m_child, a_rect, a_foundCount, a_resultCallback, a_context))
                {
                    return false; // Don't continue searching
                }
            }
        }
    }
    else // This is a leaf node
    {
        for(int index=0; index < a_node->m_count; ++index)
        {
            if(Overlap(a_rect, &a_node->m_branch[index].m_rect))
            {
                DATATYPE& id = a_node->m_branch[index].m_data;

                // NOTE: There are different ways to return results.  Here's where to modify
                //if(&a_resultCallback)
                {
                    ++a_foundCount;
                    if(!a_resultCallback(id, a_context))
                    {
                        return false; // Don't continue searching
                    }
                }
            }
        }
    }

    return true; // Continue searching
}


#undef RTREE_TEMPLATE
#undef RTREE_QUAL

#endif //RTREE_H
